Lawmakers are sounding the alarm, as they prepare to return from the August recess, over the possibility that President Obama will take sweeping executive actions on immigration in a matter of days – with some Republicans warning of a renewed budget brawl if he takes that step.

“For all intents and purposes, America no longer has an immigration system. Instead, we have unsettling chaos,” Sen. Marco Rubio, R-Fla., wrote in a letter earlier this week to Obama, urging him not to go forward with unilateral action.

The administration had indicated the president plans to announce a decision around Labor Day before leaving on a trip next week to Estonia and Wales. But administration officials told the Associated Press a host of national security crises have pushed the announcement back, likely until after Obama returns.

Still, Press Secretary Josh Earnest signaled Wednesday that the White House is not backing off its general timetable. Asked whether Republican threats of retaliation would make the president think twice about taking executive actions, he said: “No, it won’t.”

“Nothing the president does is a replacement for the kind of robust solution that passed with bipartisan support through the United States Senate, but the president is determined to act where House Republicans won’t,” Earnest said.

The comments echo Obama’s stated rationale for pursuing unilateral action – that Congress will not pass comprehensive legislation, forcing his hand. The most sweeping, controversial step under consideration involves halting deportation for millions, a major expansion of a 2012 Obama program that deferred prosecutions for those brought here illegally as children. Roughly half a million have benefited from that program, known as Deferred Action for Childhood Arrivals, or DACA.

Republicans fearing that the president will take that step have in recent days warned they could use the budget process as a weapon.

In comments that have received widespread attention, Rep. Steve King, R-Iowa, told the Des Moines Register that “all bets are off” on a looming budget resolution if Obama pulls the trigger on immigration-related measures.

"If the president wields his pen and commits that unconstitutional act to legalize millions, I think that becomes something that is nearly political nuclear," King said. "I think the public would be mobilized and galvanized and that changes the dynamic of any continuing resolution and how we might deal with that."

Though GOP leaders have shown little interest in reprising the 2013 budget battle that led to a partial government shutdown, King’s comments pointed to a willingness by some on the Tea Party-aligned right to use the budget process – or “continuing resolution” -- to push back.

Rubio, while urging Obama not to go forward, also told Breitbart News that the budget vote could play a role. "I'm interested to see what kinds of ideas my colleagues have about using funding mechanisms to address this issue," he said.

There is talk among congressional conservatives to potentially attach a provision to defund the existing executive order on immigration or curb a future one -- which could prompt a fight that leads to stalemate.

The "continuing resolution" would keep the government funded as of Oct. 1. Senior House Republican leadership sources told Fox News they would like to move the measure as soon as possible, potentially sidestepping such a confrontation by moving before the president acts.

"We want to move quickly. The longer we're in town, the more the chances for shenanigans," a senior House Republican aide told Fox News.

GOP leadership would prefer to avoid another shutdown fight weeks before an election. But one senior GOP source noted there may be an effort to address conservative concerns on immigration through a separate piece of legislation.

The debate comes as the country, and states, continue to grapple with the surge of illegal immigrant children and families coming across the southern U.S. border. Rubio claimed in his letter that the “pursuit of unilateral action” has fueled that crisis and warned that another reprieve will “incentivize more people to immigrate here illegally, and significantly set back the prospects of real reform.”

The argument goes something like this: Beyond failing to fix broken immigration laws, Congress hasn't even provided the government with enough resources to fully enforce the laws already on the books. With roughly 11.5 million immigrants in the U.S. illegally -- far more than the government could reasonably deport -- the White House believes it has wide latitude to prioritize which of those individuals should be sent home.

While Obama has yet to receive the formal recommendations he's requested from Homeland Security Secretary Jeh Johnson, administration officials said the president is intimately familiar with the universe of options and won't spend much time deliberating once Johnson delivers his report.

Beyond the mass reprieve that Republicans fear, other options under consideration, such as changes to how green cards are distributed and counted, might be less controversial because of the support they enjoy from the business community and other influential groups.

Democrats, too, are watching to see what Obama does. While many have led the charge for bold action from the White House, any controversial executive action could complicate the campaigns of Democrats facing tough elections, particularly in battleground Senate races.

Sen. Jeff Sessions, R-Ala., top Republican on the Senate Budget Committee, claimed Wednesday that Senate Democrats have nevertheless been silent on the issue.

Sessions, though, said constituents will demand Congress step in.

“They will demand a Senate vote on the House bill to stop this executive amnesty. And they will hold accountable any and all in Congress who fail to resist the President’s lawless decree,” Sessions said in a statement.

Fox News' Chad Pergram and The Associated Press contributed to this report.